Integral Calculus> integration of dx/√-log x=√π with limits ...

integration of dx/√-log x=√π with limits 0 to 1
please solve it immediately

satya , 6 Years ago

Grade 12th pass

2 Answers

Deepak Kumar Shringi

Last Activity: 6 Years ago

check your question once you have written nregative inside root is it there??

jagdish singh singh

Last Activity: 6 Years ago

$\hspace{-0.75 cm}$ Let $I = \int^{1}_{0}\frac{1}{\sqrt{-\ln x}}dx\;,$ nPut $-\ln (x)=t^2$\\\\ and $x=e^{-t^2},$ Then $dx = -2te^{-t^2}dt$ and changing limits\\\\ So $I = 2\int^{\infty}_{0}e^{-t^2}dt = 2\cdot \frac{\sqrt{\pi}}{2} = \sqrt{\pi}.$\\\\ It is well known gaussian Integral or Error function.$